is called
If G and G are two groups and
is p. G G' is an onto homomorphism
then
invertible
Answers
Answer:In mathematics, given two groups, (G, ∗) and (H, ·), a group homomorphism from (G, ∗) to (H, ·) is a function h : G → H such that for all u and v in G it holds that
{\displaystyle h(u*v)=h(u)\cdot h(v)}h(u*v)=h(u)\cdot h(v)
where the group operation on the left side of the equation is that of G and on the right side that of H.
From this property, one can deduce that h maps the identity element eG of G to the identity element eH of H,
{\displaystyle h(e_{G})=e_{H}}{\displaystyle h(e_{G})=e_{H}}
and it also maps inverses to inverses in the sense that
{\displaystyle h\left(u^{-1}\right)=h(u)^{-1}.\,}h\left(u^{-1}\right)=h(u)^{-1}.\,
Hence one can say that h "is compatible with the group structure".
Older notations for the homomorphism h(x) may be xh or xh,[citation needed] though this may be confused as an index or a general subscript. In automata theory, sometimes homomorphisms are written to the right of their arguments without parentheses, so that h(x) becomes simply x h.[citation needed]
In areas of mathematics where one considers groups endowed with additional structure, a homomorphism sometimes means a map which respects not only the group structure (as above) but also the extra structure. For example, a homomorphism of topological groups is often required to be continuous.
Step-by-step explanation: